The 11th Scandinavian International Conference on Fluid Power, SICFP’09, June 2-4, 2009, Linköping, Sweden
SECONDARY CONTROLLED MULTI-CHAMBER
HYDRAULIC CYLINDER
Adj. Prof. M Linjama*, Mr. H-P Vihtanen*, Mr. A Sipola**, Prof. M Vilenius*
*
Tampere University of Technology
Dept. of Intelligent Hydraulics and Automation
FI-33101 Tampere, Finland
Phone +358 3 3115 11, Fax +358 3 3115 2240
E-mail: matti.linjama@tut.fi
*
Norrhydro Oy, Rovaniemi, Finland
ABSTRACT
Hydraulic cylinder with adjustable piston area is a dream generally considered as impossible.
It could allow energy optimal four-quadrant secondary control of linear actuator, for example.
Although continuously adjustable piston area is difficult or even impossible, discrete
adjustability is possible. A simple example is two cylinders connected in parallel. This paper
presents an integrated multi-chamber hydraulic cylinder having sixteen effective piston areas.
The four-quadrant secondary control of a hydraulic axis is implemented and experimentally
tested. The approach is new and the authors know no similar research publications. The
hydraulic hardware is simple having high-pressure and low-pressure lines, multi-chamber
cylinder and logic valves. Results show over 60 percent reduction in power losses when
compared to the traditional load sensing system because of energy recovery and minor
throttling losses. Controllability is good at higher velocities but some challenges exist at low
velocities.
KEYWORDS: Multi-chamber cylinder, secondary control, energy efficiency
1 INTRODUCTION
Secondary control is one of the most efficient control methods for hydraulic motors [1, 2]. Its
main benefits are simple hydraulic circuit (common constant pressure line), no throttling
losses, and energy recovery e.g. during braking or lowering the load. The principle of the
secondary control is to control torque of the hydraulic motor by controlling the displacement
of the motor. As variable displacement unit is needed, the principle is considered as
impossible for hydraulic cylinders. This paper shows that secondary controlled hydraulic
cylinder can be implemented successfully by utilizing multi-chamber cylinder approach.
Normal hydraulic cylinder has two chambers and multi-chamber cylinder is defined in this
paper as cylinder having more than two chambers. The simplest case is three-chamber
cylinder shown in Figure 1 (a). The most common application of this structure is to
implement symmetric cylinder without extra rod [3, 4]. Other applications are to use the third
chamber for balancing the hydraulic load [5] or synchronizing movements of other actuators
[6]. Two variants of the four-chamber cylinder are shown in Figure 1 (b) and (c). The first
version is known e.g. in [7] and its good point is highly integrated structure. The second
version has two traditional cylinders connected in parallel.
Figure 1. Different multi-chamber cylinders: three chamber cylinder (a), integrated
four-chamber cylinder (b), and four-chamber cylinder composed of two traditional
cylinders (c).
Typical control approach of the multi-chamber cylinder is to implement the normal valve
control by using two chambers, and to use the other chamber(s) for some other purpose. This
is understandable approach, because traditional valves are designed for traditional cylinders.
The digital hydraulics approach [8] implements every control edge individually by parallel
connected on/off valves. All functionality is in the software and the approach sets no
limitations for the number of control edges. In the case of the multi-chamber cylinder, it may
be enough to connect each chamber into supply line or tank line via single on/off valve, which
results in stepwise controllability of the piston force. This approach is studied in this paper
and the four chamber cylinder of Fig. 1 (b) is selected as the test case. The target is to
implement four-quadrant secondary control, to show that the approach works, and to study
controllability and energy efficiency of the system.
2 SECONDARY CONTROLLED FOUR-CHAMBER CYLINDER
Consider the four-chamber cylinder and control valve system depicted in Figure 2. The
system has two constant pressure hydraulic sources/sinks: high-pressure line (HP) and lowpressure line (LP). Each chamber of the cylinder can be connected to either HP or LP line via
on/off logic valves. The piston areas are selected to be in ratios AA:AB:AC:AD = 8:4:2:1 and the
cylinder force is given by:
F = AA pA − AB pB + AC pC − AD pD
(1)
If the pressure losses of the on/off valves are small, the pressure in A-chamber can be
approximated as:
⎧ p , if uHP − A = 1 & uLP − A = 0
p A ≈ ⎨ HP
⎩ pLP , if uHP − A = 0 & uLP − A = 1
(2)
and the other chamber pressures can be approximated similarly. It is clear that Eq. 2 is valid
only when the piston velocity is so small that pressure losses at on/off valves are negligible.
Figure 2. A four-chamber cylinder with control valves.
Now the cylinder has sixteen different forces depending on the state of on/off valves and
pressures at HP and LP lines. Figure 3 shows these forces in the order of magnitude for some
different pressures when the piston areas are AA = 3200 mm2, AB = 1600 mm2, AC = 800 mm2,
AD = 400 mm2. It is important to note that the forces are evenly spaced with any HP and LP
pressure combinations. A drawback of the “8:4:2:1” design is that the negative force
generated by the cylinder is relatively small.
The four chamber cylinder can be considered as a force actuator with 16 discrete output
values. When connected to the inertia load, the system is principally a double integrator with
quantized actuator output. Thus, velocity feedback is essential in order to stabilize the system.
As a position tracking is studied in this paper, the position feedback is needed as well. In
order to compensate for the unknown load force, PI-controller is used in the position loop.
The integrator introduces overshoot in the position response, but it can be compensated by
modifying the reference, for example. The block diagram of the control system is shown in
Figure 4.
Figure 3. Different forces of a four chamber cylinders with different HP and LP
pressures. Piston areas are AA = 3200 mm2, AB = 1600 mm2, AC = 800 mm2,
AD = 400 mm2.
pHP
vref
pLP
xref
+
–
PIController
+
+
–
Kv
Fref
Selection of
the control
combination
x
u
System
v
Figure 4. Block diagram of the control system.
The simplest way to select the control combination of valves is to select the combination
which has the smallest force error. All 16 forces can be calculated from Eq. 1, if HP and LP
pressures are measured and if Eq. 2 holds. Thus, the HP and LP pressures must be measured
or known as shown in Figure 4. The simple selection according to the force error may result
in unnecessary switching between two control combinations. Thus, the selection is made by
minimizing the following penalty function:
J ( unew , u prev ) = Fref − Fˆ ( unew ) + WSW Δu
⎧⎪1 , if unew ≠ u prev
Δu = ⎨
⎪⎩0 , if unew = u prev
(3)
where uprev is the previous control combination and unew is the new control combination to be
determined. F̂ is the calculated force estimate of the control combination unew, and the
switching term WswΔu causes that the control combination changes only, if some other control
combination gives significantly smaller force error. The value of the penalty function is
calculated for all 16 control combinations and the combination, which minimizes the function,
is selected. The parameter WSW is tuned to find proper compromise between control activity
and control performance.
One special feature of the force controlled system with discrete output is that it is difficult to
maintain any constant velocity because each discrete force causes acceleration or deceleration
of the load. This implies that it is impossible to stop the movement with the control system of
Fig. 4, but the stopping situation must be handled separately. The movement stops when all
valves are closed and this stop mode is enabled if the following conditions hold:
xref − x ≤ xtol1 AND
vref ≤ vtol
(4)
The force controller is enabled again if the following conditions hold:
xref − x > xtol 2 OR
vref > vtol
(5)
Note that hysteresis is introduced by using two different position error thresholds, xtol1< xtol2.
The integrator of the PI-controller is disabled when the system is in the stop mode.
Yet one thing, which must be considered, is short circuit flow through valves. The finite valve
dynamics cause that both valves are partly open for a short period, if they are commanded to
change their state simultaneously. This causes short circuit flow and increases losses. In order
to avoid this, the opening of all valves is delayed by 6 ms.
3 TEST SYSTEM
The test system is shown in Figure 5. The mechanism is the same as in [9, 10, 11] and
cylinder kinematics is also almost the same. The controllability and energy consumption of
the system has been measured with a mobile proportional valve in the constant supply
pressure and load sensing mode, and this data is used as a reference. Three loading conditions
are studied:
•
•
•
Loading A: m1=200 kg, m2=150 kg, m3=50 kg, m4 = 0 kg (almost balanced)
Loading B: m1=200 kg, m2=0 kg, m3=200 kg, m4 = 0 kg (restrictive load)
Loading C: m1=100 kg, m2=200 kg, m3=0 kg, m4 = 100 kg (overrunning load)
The cylinder diameters are 85/63/40/28 mm giving piston areas of AA = 5059 mm2, AB = 2557
mm2, AC = 1257 mm2, AD = 641 mm2. The nominal pressures are selected to be pHP = 16 MPa
and pLP = 2 MPa, which gives the minimum and maximum cylinder forces of -38.5 kN and
94.6 kN, respectively.
The test trajectory consists of two upwards and two downwards movements. Movement time
is 1.25 s and the start point of the trajectory and movement amplitudes are selected such that
joint angles are the same as in earlier publications. The main difference to the earlier
publications is that the fourth order polynomial is used as a position reference instead of the
fifth order polynomial in order to reduce the overshoot caused by the integrator. However, as
the movement time and movement amplitudes are the same, the results can still be compared.
Hydac WS08W-01 direct operated solenoid valves are used as the control valves as shown in
Figure 5. The valve is bi-directional and its flow capacity is about 12 l/min at 0.5 MPa
pressure differential. The parallel connected valves are used in chambers A and B in order to
minimize flow losses. Valves are equipped with 12 VDC coil and control electronics is based
on H-bridge configuration with Texas Instruments DRV102T high-side PWM driver and
International Rectifier IRLR120N low-side FET. Supply voltage is 48 V, pull-on time is 6.8
ms and PWM duty ratio is about 20 percent. This gives opening and closing delays of 8-10
ms.
The measurements consist of piston position, chamber pressures, input current of control
electronics, HP and LP pressures, and flow rates at HP and LP lines. Druck PTX1400 sensors
(40 MPa, 4-20 mA) are used as pressure sensors and pressures are measured from the valve
assembly. Piston position is measured by a linear potentiometer.
A small fixed displacement pump with bypass valve is used to satisfy the average power
requirement of the system and the peak power is taken from the HP and LP accumulators. The
bypass valve is closed when the measured HP pressure drops below 15.7 MPa and opened
again when the pressure exceeds 16.3 MPa. The LP pressure is implemented by a pressure
relief valve. The hydraulic circuit is not fully optimized because lots of hoses are used. The
capacitance and inductance of hoses have clear effect on the energy consumption and pressure
dynamics at cylinder chambers.
The input and output power and energy are used in the analysis of losses. The hydraulic input
power of the system is calculated as follows
Pin = pHPQHP + pLPQLP
(6)
where the positive flow direction is towards the system. The output power of the actuator is
defined as:
Pout = ( AA pA − AB pB + AC pC − AD pD ) v
where v is piston velocity. Power loss is defined as Pin – Pout.
(7)
Figure 5. Test system.
4 EXPERIMENTAL RESULTS
4.1 Signal Conditioning
Proper controller implementation requires careful signal conditioning. Therefore, the
measured signals are low-pass filtered as follows:
1) The signal conditioning is made with 2 ms sampling time while the controller runs
with 12 ms sampling time.
2) All signals are filtered using five point α-trimmed mean filter, i.e. five data points are
buffered, the biggest and smallest values are removed and the mean of remaining three
is outputted.
3) All signals are filtered with the second order discrete time filter having damping factor
of 0.8.The break frequency is 30 Hz for position and 5 Hz for pressures.
4) Velocity estimate is obtained by differentiating the low-pass filtered position signal
and taking mean value of five points.
4.2 Tuning of Controller
The tuning is made experimentally by keeping in mind that each gain is at maximum half of
the critical gain. The weight for valve switching (see Eq. 3) is selected to be as big as possible
such that the control performance does not degrade significantly. The position tolerances (see
Eqs. 4 and 5) are selected such that no limit cycles exist. The controller parameters are given
in table 1.
Table 1. Parameters of the controller.
Parameter
Description
Sampling time
TS
Velocity feedback gain, see Fig. 4
Kv
P term gain of the PI-controller, see Fig. 4
KP
I term gain of the PI-controller, see Fig. 4
KI
Weight for valve switchings, see Eq. 3
WSW
xtol1
Position error threshold to enter the stop mode, see Eq. 4
xtol2
Position error threshold to escape the stop mode, see Eq. 5
Velocity reference threshold to enter/escape the stop mode,
vtol
see Eq. 4
Value
12 ms
4.5×105 N/(m/s)
9.5 1/s
4.0 1/s2
3000 N
1.0 mm
1.5 mm
0.1 mm/s
4.3 Measured Reponses
Figure 6 depicts the measured response for Loading B, i.e. for restricting load. The dynamic
behavior is good especially in the faster response. Chamber pressures and force behaves
relatively smoothly but there are significant pressure oscillations in the HP and LP pressure
caused by pipeline dynamics. Figure 7 shows the measured response for Loading C, i.e. for
overrunning load. The dynamic performance is similar but the control output saturates at t ≈ 8
s (A and C are connected to LP, B and D to HP), and the cylinder runs at maximum negative
force. At the same time, the piston moves at high velocity causing significant valve losses,
and the pump pressure drops because of line losses and relatively small HP accumulator.
These facts cause big force error and it can be concluded that the cylinder can just handle the
negative Loading C. These measurements show clearly that the system is capable for fourquadrant and energy efficient motion control. Significant energy recovery exists, and the load
force seems to have no effect on losses.
Figure 6. Measured response for Loading B.
Figure 7. Measured response for Loading C.
4.4 Meaasured Eneergy Losses
The fairr comparisoon of energyy losses is slightly com
mplicated because
b
the system stu
udied has
non-zerro tank presssure. The mean
m
energyy flow of th
he system is
i from HP line to LP line and
the meaan LP flow
w is out froom the systtem. Normaal hydraulic pumps cannot tolerate high
suction pressures and
a the LP pressure must
m
be driv
ven into thee zero-presssure tank th
hrough a
pressuree relief valvves. This is why two looss values are
a calculateed, one accoording to Eq. 6 (i.e.
LP pow
wer is recoovered at pump)
p
and one witho
out term pLPQLP (i.e. LP powerr is not
recovereed). Accum
mulator lossses are ignored in thee analysis and
a it is asssumed thaat this is
compennsated becaause of mucch smaller pump lossses (only sm
mall pumpp is needed
d). Some
variation occurs in the power consumptio
c
on and the average
a
of fiive measureements is prresented.
All signnals are low
w-pass filtereed with a seecond orderr filter with 10 Hz breaak frequenccy before
calculattion of poweer losses.
The refference system consists of the same
s
mechanism, twoo parallel cconnected cylinders
c
(63/36-2200), variabble displacement pum
mp, and Bosch Rexrotth M4-12 m
mobile prop
portional
valve [110]. The puump runs inn either connstant pressure mode or in LS m
mode. The constant
supply pressure
p
is selected to be 12 MPa such that th
he force rannge of the aactuator is about
a
the
same. Inn the LS moode, the pum
mp pressuree is adjusted
d to be 1 MPa more thaan the meassured LS
pressuree of the valvve.
Figure 8 shows thhe measuredd energy loosses. On average, thhe secondarry controlled multichambeer cylinder reduces
r
the input energgy by 76 peercent whenn compared to the prop
portional
valve coontrolled acctuator withh constant suupply pressure, and byy 62 percentt when com
mpared to
the propportional LS
S actuator. If the LP power
p
canno
ot be recoveered, the coorrespondin
ng values
are 71 and
a 53 perccent. Becauuse the typical LS sysstem has several actuattors and thee supply
pressuree can be opptimized forr one actuaator only, it can be estiimated thatt the multi-cchamber
cylinderr approach reduces
r
lossses at least 60
6 percent.
1
16
1
14
1
12
Proportionaal valve, pP = 12
1 MPa
Loss [kJ]
1
10
Proportionaal valve, LS
8
6
Multi-cham
mber cylinder without
w
LP recoveryy
4
Multi-cham
mber cylinder with
w LP
recovery
2
0
Load
ding A
Loading B
Loading C
ulic energy losses for proportion
p
nal valve an
nd multi-ch
hamber
Figuree 8. Measurred hydrau
cylinder.
5 DISCUSSION
5.1 Controllability Compared to Traditional Valve Controlled System
The concept presented is completely different from traditional valve controlled systems. The
cylinder is force source and has no hydraulic stiffness, for example. This implies that there are
no natural frequency and corresponding oscillations except in the stop mode, which is clearly
seen in the measured responses. The control principle requires inertia load and controllability
improves with increasing inertia contrary to traditional systems. Thus, the concept is best
suited for high inertia systems.
5.2 Electric and Friction Losses
Figure 8 does not include the electric valve losses. These losses are measured for loadings A
and B, and are 0.35 kJ for loading A and 0.27 kJ for loading B. The measurement failed for
loading C but it can be assumed that the electric valve losses are about the same. The electric
valve losses of the proportional valve are not measured but can be assumed to be about 0.06
kJ (12 W for five seconds). Thus, the difference between electric losses is about 0.25 kJ and
quite insignificant. The difference will vanish when the “second generation” on/off valves
come into market. Another topic, which is not included in Fig. 8, is the friction of the
cylinder. It is clear, that the friction is higher in the multi-chamber cylinder. In this case, the
friction losses can be estimated directly from the output energy, because the system does no
mechanical work. The output energy is about 0.2 kJ for the traditional cylinder and about 0.4
kJ for the multi-chamber cylinder. Thus, the friction seems to play only a minor effect in the
system studied.
5.3 Sources of Hydraulic Losses in Multi-Chamber Cylinder
The most important sources of losses are flow losses in valves, flow losses in hoses, and
compressibility losses. The compressibility losses are caused by the fact that the energy stored
in hydraulic capacitance is lost when the chamber switches from HP to LP. These losses
vanish, when the pressure difference between HP and LP pressure approaches zero. Thus, the
compressibility losses can be estimated by measuring energy consumption with different HP
pressures. Figure 9 shows the measured energy losses for Loading B with different HP
pressures. When the HP pressure drops by 6 MPa, the losses reduce by 1.4 kJ. From this, it
can be concluded that the compressibility losses are over 2 kJ and thus the most important
source of losses.
The flow losses of valves can be estimated from the known valve resistances and known
velocity profile. This calculation gives valve losses of about 0.5 kJ, from which two third
occurs in the control edges of the A-chamber. The remaining losses occur in hoses, pipes and
fitting. These losses are caused mainly by the high viscosity of the oil. The losses of the
system are so low that it is impossible to heat up the oil above 25 °C, and the oil viscosity
remains at 90 cSt.
4
3,5
Loss [kJ]
3
2,5
2
1,5
1
0,5
0
p
p_HP
= 16 MPaa
p_HP = 14
1 MPa
p__HP = 12 MPa
p_HP = 10
0 MPa
Figuree 9. Measurred hydrau
ulic energy losses for Loading
L
B with
w different HP preessures.
5.4 Min
nimization of
o Compresssibility Lossses
The com
mpressibilitty loss occcurs every time when
n the chambber switchees from HP
P to LP
pressuree. The energgy stored inn a linear hyydraulic capacitance Ch is
1
WC = Ch p 2
2
from whhich it folloows that the energy losss of the HP to LP switcching is
1
2
2
WC ,loss = Ch ( pHP
− pLLP
)
2
(8)
(9)
Thus, thhe loss is proportionaal to hydraaulic capaciitance. In the
t system studied, th
he hoses
dominatte the hydrraulic capaacitances off the cham
mbers, see Fig.
F
5. Figure 10 dep
picts the
theoretical hydraullic capacitannces in twoo cases. In the
t first casse hoses of Fig. 5 are included
i
t second case
c
all hosses are shorttened to 0.4
4 m. The buulk moduli oof oil and hoses
h
are
and in the
assumedd to be 12200 MPa and
a
600 MPa,
M
respecctively. Figgure 10 shoows that hydraulic
h
capacitaances and compressibi
c
ility losses can be redu
uced by appproximatelyy 50 percen
nt in the
system studied.
Figure 10. Theoretical hydraulic capacitances as a function of piston position with
original hoses (left) and shortened hoses (right).
6 CONCLUSIONS
Results show that the secondary controlled multi-chamber cylinder saves very much energy
when compared to the traditional solutions. The solution has practically no throttling losses, it
automatically recovers negative mechanical power, and it uses constant supply pressure. The
constant supply pressure implies that the efficiency remains good also in the multi-actuator
systems contrary to the traditional load sensing system. The system is simple consisting of the
multi-chamber cylinder, logic valves, two constant pressure lines and force-based control
algorithm. The controllability is also good especially at higher velocities if the inertia of the
system is big enough.
The first experimental results show about 60 percent reduction in losses when compared to
the traditional load sensing actuator, and the optimization of the system should still improve
the energy efficiency. It is expected that the energy saving is significantly bigger in the multiactuator systems because constant supply pressure can be used. The experimental results show
also that only a tiny pump is needed in order to satisfy average power requirement of the
actuator. This is big advantage when compared to other approaches, which require pump
dimensioning according to the peak power.
The approach is new and has some challenges as well. The controllability at low velocities is
not yet as good as with the well-tuned proportional valve, and it must be improved by using
more sophisticated controllers, for example. The switching behavior needs also more careful
research and the research topics include the effect of valve size, piston position, hydraulic
capacitances and inductances on the losses and pressure dynamics at cylinder chambers.
Safety is also important to take into account. The force controlled cylinder cannot be used
without feedback, and large valves, which are needed to reduce losses, yield very high
maximum velocity of the cylinder.
To conclude, a new energy efficient way to control multi-chamber cylinder has been
introduced and experimentally tested. The first results are very promising but (as always)
further research is needed.
The methods described in this paper are protected by an international patent application.
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